How to calculate multi-step prediction intervals for time series data? I need to manually calculate multi-step prediction intervals for time series data. I know packages like 'forecast' in R provide these, but I cannot use these packages as the production infrastructure does not support R. 
Could someone point me to an article that explains how to generate multi-step prediction intervals? 
 A: I cannot point you to an article, but I can point you towards a book if that counts!? The book is called "Forecasting with Univariate Box - Jenkins Models: Concepts and Cases" by Alan Pankratz (1983). Chapter 10 of the book is titled "Forecasting" and not only does the chapter go through the algebra of ARIMA forecasts, but it also explains the dispersion of ARIMA forecasts, forecast confidence intervals, forecasting from data in log form, and most helpfully, there are numerical examples.
I've typed up a short document (the link goes to a .pdf file on dropbox.com) that should give you a fair idea about how to calculate prediction intervals. I hope you find it helpful.
A: Gardner gives advice and several references in his "Exponential smoothing - state of the art - Part II," paper of 2005. I hesitate to give a link, but you can find it. Check in section 4.4, which focuses on variance and prediction intervals. You might also look for "Prediction Intervals for exponential smoothing using two new classes of state space models," by Hyndman, Koehler, Ord, and Snyder in the Journal of Forecasting (2005), 24, 17-37. 
